a. What is the probability that the sample mean commute distance is greater than 13 miles?

Question

Going to work: An ABC News report stated that the mean distance that commuters in the United States travel each way to work is 16 miles. Assume the standard deviation is 8 miles. A sample of 75 commuters is chosen

Answer 1

mean is normally distributed with mean 16, SD 8. sample size is 75.

standard error of mean 16/sqrt(75) = 1.85

want to find P(xbar > 13)

transform to standard normal, using z = (xbar - pop mean)/std error = (xbar - 16)/1.85

P(x bar > 13) = P(z > (13-16)/1.85) = P(z > -1.62) = 1 - P(z < -1.62) = 1 - 0.0526 = 0.9474.